Theorem spesbcd 3522

Description: form of spsbc 3448. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypothesis

Ref	Expression
spesbcd.1	|- ( ph -> [. A / x ]. ps )

Assertion

Ref	Expression
spesbcd	|- ( ph -> E. x ps )

Proof of Theorem spesbcd

Step	Hyp	Ref	Expression
1		spesbcd.1	. 2 |- ( ph -> [. A / x ]. ps )
2		spesbc 3521	. 2 |- ( [. A / x ]. ps -> E. x ps )
3	1, 2	syl 17	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1704   [.wsbc 3435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rex 2918  df-v 3202  df-sbc 3436

This theorem is referenced by:  euotd  4975  ex-natded9.26  27276  bnj1465  30915  bj-sels  32950  spesbcdi  33925  brtrclfv2  38019  cotrclrcl  38034